1. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Scientific Method The scientific method is a logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating theories that are supported by data. Section 1 Scientific Method

2. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Observing and Collecting Data Observing is the use of the senses to obtain information. data may be qualitative (descriptive) quantitative (numerical) A system is a specific portion of matter in a given region of space that has been selected for study during an experiment or observation. Section 1 Scientific Method

3. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Formulating Hypotheses Scientists make generalizations based on the data. Scientists use generalizations about the data to formulate a hypothesis, or testable statement. Hypotheses are often “if-then” statements. Section 1 Scientific Method

4. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Testing Hypotheses Testing a hypothesis requires experimentation that provides data to support or refute a hypothesis or theory. Controls are the experimental conditions that remain constant. Variables are any experimental conditions that change. Section 1 Scientific Method

5. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Scientific Method Section 1 Scientific Method

6. Chapter 2 © Houghton Mifflin Harcourt Publishing Company SI Measurement Scientists all over the world have agreed on a single measurement system called Le Système International d’Unités, abbreviated SI. Section 2 Units of Measurement SI has seven base units most other units are derived from these seven

7. Chapter 2 © Houghton Mifflin Harcourt Publishing Company SI Base Units Section 2 Units of Measurement

8. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Conversion Factors A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other. example: How quarters and dollars are related Section 2 Units of Measurement

9. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Conversion Factors, continued Dimensional analysis is a mathematical technique that allows you to use units to solve problems involving measurements. Section 2 Units of Measurement quantity sought = quantity given × conversion factor example: the number of quarters in 12 dollars number of quarters = 12 dollars × conversion factor

10. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Using Conversion Factors Section 2 Units of Measurement

11. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Lesson Starter Look at the specifications for electronic balances. How do the instruments vary in precision? Discuss using a beaker to measure volume versus using a graduated cylinder. Which is more precise? Section 3 Using Scientific Measurements

12. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Accuracy and Precision Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. Precision refers to the closeness of a set of measurements of the same quantity made in the same way. Section 3 Using Scientific Measurements

13. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Accuracy and Precision Section 3 Using Scientific Measurements

14. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Accuracy and Precision, continued Percentage Error Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100. Section 3 Using Scientific Measurements ×

15. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Accuracy and Precision, continued Sample Problem C A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement? Section 3 Using Scientific Measurements

16. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Accuracy and Precision, continued Sample Problem C Solution Section 3 Using Scientific Measurements

17. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Accuracy and Precision, continued Error in Measurement Some error or uncertainty always exists in any measurement. skill of the measurer conditions of measurement measuring instruments Section 3 Using Scientific Measurements

18. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Significant Figures Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. The term significant does not mean certain. Section 3 Using Scientific Measurements

19. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Reporting Measurements Using Significant Figures Section 3 Using Scientific Measurements

20. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Significant Figures, continued Determining the Number of Significant Figures Section 3 Using Scientific Measurements

21. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Significant Figures, continued Sample Problem D How many significant figures are in each of the following measurements? a. 28.6 g b. 3440. cm c. 910 m d. 0.046 04 L e. 0.006 700 0 kg Section 3 Using Scientific Measurements

22. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Sample Problem D Solution a.28.6 g There are no zeros, so all three digits are significant. b. 3440. cm By rule 4, the zero is significant because it is immediately followed by a decimal point; there are 4 significant figures. c. 910 m By rule 4, the zero is not significant; there are 2 significant figures. Significant Figures, continued Section 3 Using Scientific Measurements

23. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Sample Problem D Solution, continued d. 0.046 04 L By rule 2, the first two zeros are not significant; by rule 1, the third zero is significant; there are 4 significant figures. e. 0.006 700 0 kg By rule 2, the first three zeros are not significant; by rule 3, the last three zeros are significant; there are 5 significant figures. Significant Figures, continued Section 3 Using Scientific Measurements

24. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Significant Figures, continued Addition or Subtraction with Significant Figures When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. Addition or Subtraction with Significant Figures For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. Section 3 Using Scientific Measurements

25. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Sample Problem E Carry out the following calculations. Express each answer to the correct number of significant figures. a. 5.44 m - 2.6103 m b. 2.4 g/mL  15.82 mL Significant Figures, continued Section 3 Using Scientific Measurements

26. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Sample Problem E Solution a.5.44 m - 2.6103 m = 2.84 m Significant Figures, continued There should be two digits to the right of the decimal point, to match 5.44 m. b. 2.4 g/mL  15.82 mL = 38 g There should be two significant figures in the answer, to match 2.4 g/mL. Section 3 Using Scientific Measurements

27. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Significant Figures, continued Conversion Factors and Significant Figures There is no uncertainty exact conversion factors. Most exact conversion factors are defined quantities. Section 3 Using Scientific Measurements

28. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Using Sample Problems Analyze The first step in solving a quantitative word problem is to read the problem carefully at least twice and to analyze the information in it. Plan The second step is to develop a plan for solving the problem. Compute The third step involves substituting the data and necessary conversion factors into the plan you have developed. Section 3 Using Scientific Measurements

29. Chapter 2 © Houghton Mifflin Harcourt Publishing Company Using Sample Problems, continued Evaluate Examine your answer to determine whether it is reasonable. 1. Check to see that the units are correct. 2. Make an estimate of the expected answer. 3. Check the order of magnitude in your answer. 4. Be sure that the answer given for any problem is expressed using the correct number of significant figures. Section 3 Using Scientific Measurements